# Do Closed Timelike Curves Exist?

1. Aug 9, 2008

### twoface42

im doing my project for school on this a need help.

2. Aug 9, 2008

### JesseM

For reference, twoface42 and I already had some discussion of this by PM, so people can see if they have anything they want to add or if I made any mistakes in my comments:
and on a question about the Kerr metric:
And in response to a question about whether any CTCs in a rotating black hole would be sealed off from the outside universe:
And one other thing I wasn't sure about:

Last edited by a moderator: May 3, 2017
3. Aug 9, 2008

### George Jones

Staff Emeritus
At what level are you in school?

Adding a little to what JesseM wrote, here

are some general thoughts on time travel, including a little on
It seems that we won't know the role of quantum gravity until we have a workable quantum theory of gravity.

Here

is a mathematical demonstration of closed timelike curves in the spacetime of a rotating black hole. There does exists a closed timelike curve through any event inside the inner horizon, but I am not sure if all of these curves pass through the ring. Israel and Poisson (and others) have done work on what happens inside rotating black holes that might be relevant.

Here

is a proof that any compact (in the mathematical sense) spacetime contains closed timelike curves.

Last edited: Aug 11, 2008
4. Aug 9, 2008

### MeJennifer

A chicken and egg argument. A Kerr metric is a vacuum solution so there is nothing available to perturb. If you assume a spacetime with such additional mass-energies then you obviously cannot use the Kerr metric. And weak field approximations are obviously useless in those models since the curvature is too strong for that.

Same chicken and egg argument as above, if the spacetime contains radiation the Kerr solution is obviously the wrong solution.

5. Aug 9, 2008

### JesseM

A perturbation of the Kerr metric would obviously result in a somewhat different metric, but that's what perturbation means, you're making a slight change and seeing the result. I imagine this is different from the weak-field approximation, since as you say spacetime is highly curved in the neighborhood of a rotating black hole. Physicists do talk about perturbations of the Kerr metric...for example, this book says:
Likewise, have a look at the first page of http://www.jstor.org/pss/79484, which considers "linear perturbations of black hole models by a variety of fields" and uses this to "discuss the internal stability of the Kerr and Reissner-NordstrÃ¶m black hole solutions", saying "These models have highly peculiar, if not disturbing, features in their interiors. The question we would like to be able to answer is whether these features actually manifest themselves in nature or are purely a product of the exact symmetry of the model".

Other papers discussing the stability of Kerr black holes against perturbations:

http://www.jstor.org/pss/78810

http://arxiv.org/abs/gr-qc/9803004

http://arxiv.org/abs/gr-qc/9902008

Last edited by a moderator: Apr 23, 2017
6. Aug 9, 2008

### JesseM

When looking for information on Kerr black holes and CTCs, I came across this paper which suggests that the apparent CTCs are just an artifact of a bad choice of coordinates, and with a different choice they disappear (and so are not really physical):

http://arxiv.org/abs/gr-qc/0207014

If you feel like giving it a once-over, I'd be interested to know if you think the argument can be dismissed out of hand, or if there could possibly be something to it.

7. Aug 9, 2008

### twoface42

JesseM so the paper you sent me kind of confussed me,does it say ctc's are real or not?

8. Aug 9, 2008

### JesseM

The paper I just posted above claims to show that they don't actually happen inside the inner event horizon of the Kerr metric for a rotating black hole. But papers on arxiv.org are not peer-reviewed, and this claim contradicts a lot of previous studies of the Kerr metric, so I'd be cautious about accepting it.

9. Aug 10, 2008

### twoface42

you said the paper condradicts other's,like what?, you also said the claims show that they don't actually happen inside the inner event horizon of the Kerr metric for a rotating black hole,do they appear in some other region of a black hole or not at all?

10. Aug 10, 2008

### JesseM

All the previous papers and books which try to prove the Kerr metric does contain CTCs...George Jones linked to this post which is based on a textbook, for example. You can find a lot of other examples if you do a google search like this one.
According to the author of that paper, not at all.

11. Aug 10, 2008

### twoface42

i was also told that kerr's metric doesnt take into consideration quantum mechanics,is that why most people think quantum gravity will eliminate ctc's?

12. Aug 10, 2008

### JesseM

It's why it's seen as a possibility that quantum gravity might give different predictions about CTCs, but there are more specific hints that CTCs will be ruled out by quantum gravity too--did you read the links in my first post, or in the post by George Jones? I would also be curious about the answer to George Jones' question about what level you are in school.

13. Aug 10, 2008

### twoface42

i am in my 2nd year of college.is there anything else used against ctc's?

14. Aug 10, 2008

### JesseM

And what is the specific class that this is for? What's your exact assignment? What types of sources are you expected to use to research it?

15. Aug 10, 2008

### twoface42

you said quantum mechanics might give different predictions on ctc's,what kind?

16. Aug 10, 2008

### JesseM

Last edited by a moderator: May 3, 2017
17. Aug 11, 2008

### twoface42

it's special and general relativity class,and im supposed to get all the info on the solution's of GR

18. Aug 11, 2008

### JesseM

But you're not required to understand any of the math of these solutions? And where are you supposed to get the information? Presumably they don't expect you to do all the research on online forums.

19. Aug 11, 2008

### twoface42

i was given this,what does this mean? The Kerr vacuum is unobjectionable and realistic (for black hole models) in the exterior regions, and unobjectionable but perhaps unrealistic (for black hole models) in the "shallow interior" regions, but as several commentators have mentioned, it is objectionable in the "deep interior" regions, since it there admits closed timelike curves (CTCs), as does the Goedel lambdadust. These CTCs are problematical.

20. Aug 11, 2008

### JesseM

Could you answer my questions about the nature of the assignment? And how soon is it due? If not too soon they probably want you to look at some actual books...

21. Aug 11, 2008

### twoface42

thursday and present on friday.

22. Aug 11, 2008

### George Jones

Staff Emeritus
Take a look at this paper and the works that it references:

http://arxiv.org/abs/gr-qc/0204022.

Also, according to the work of Poisson and Israel, classical physics might block the formation of closed timelike curves in Kerr spacetime. They show that a test fluid that has fallen into the black hole has an energy density that diverges at the inner (Cauchy) horizon according to some local observers. Problem 3 on pages 217-18 of Poisson's book A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics demonstrates this for a Reissner-Nordstrom black hole, which has a Cauchy horizon, but which doesn't have closed timelike curves. Poisson hints that the situation is similar for Kerr, but a little more complicated mathematically.
This looks interesting, but I'm not sure when/if I'll be able to have a close look at it. As you (Jesse) said, caution is needed. Since this is an extraordinary result for which a journal reference can't be found, I suspect this paper has been rejected by several journals. The abstract statement
to me seems impossible. Kerr-Newman is a maximally extended spacetime and changing coordinates does not change the causal character of a curve.

Wormholes can also be used to generate closed timelike curves, but wormholes require exotic material. I wrote about Morris-Thorne wormholes and closed timelike curves here:

Last edited: Aug 11, 2008
23. Aug 11, 2008

### twoface42

would ctc's split other universes?

24. Aug 11, 2008

### twoface42

george jones,so those two authors you told say classical physics will prevent ctc's from forming?

25. Aug 11, 2008

### JesseM

And how long ago were you first given this assignment? Unless it's very short-term I'd think your professor would expect you to have read some books for it rather than just asking questions online.